On the study of catalytic membrane reactor for water detritiation: Modeling approach

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On the study of catalytic membrane reactor for water

detritiation: Modeling approach

Karine Liger, Jérémy Mascarade, Xavier Joulia, Xuan Mi Meyer, Michèle

Troulay, Christophe Perrais

To cite this version:

Karine Liger, Jérémy Mascarade, Xavier Joulia, Xuan Mi Meyer, Michèle Troulay, et al.. On the

study of catalytic membrane reactor for water detritiation: Modeling approach. Fusion Engineering

and Design, Elsevier, 2016, 109-111, pp.1412-1416. �10.1016/j.fusengdes.2015.12.009�. �hal-01877225�

To cite this version :

Liger, Karine and Mascarade, Jérémy and Joulia, Xavier

and Truong-Meyer, Xuân-Mi

and Troulay, Michèle and Perrais, ChristopheOn the

study of catalytic membrane reactor for water detritiation: Modeling approach. (2016)

Fusion Engineering and Design, 109-111. 1412-1416. ISSN 0920-3796

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pen

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rchive

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On the study of catalytic membrane reactor for water detritiation:

Modeling approach

Karine Liger

a,∗

_{, Jérémy Mascarade}

a

_{, Xavier Joulia}

b,c

_{, Xuan-Mi Meyer}

b,c

_,

Michèle Troulay

a

_{, Christophe Perrais}

a

a_{CEA, DEN, DTN/SMTA/LIPC Cadarache, Saint Paul-lez-Durance F-13108, France}

b_{Université de Toulouse, INPT, UPS, Laboratoire de Génie Chimique, 4, Allée Emile Monso, Toulouse F-31030, France} c_{CNRS, Laboratoire de Génie Chimique, Toulouse F-31030, France}

•_{Experimental results for the conversion of tritiated water (using deuterium as a simulant of tritium) by means of a catalytic membrane reactor in view}

of tritium recovery.

•_{Phenomenological 2D model to represent catalytic membrane reactor behavior including the determination of the compositions of gaseous effluents.} •_{Good agreement between the simulation results and experimental measurements performed on the dedicated facility.}

•_{Explanation of the unexpected behavior of the catalytic membrane reactor by the modeling results and in particular the gas composition estimation.}

In the framework of tritium recovery from tritiated water, efficiency of packed bed membrane reactors have been successfully demonstrated. Thanks to protium isotope swamping, tritium bonded water can be recovered under the valuable Q2form (Q = H, D or T) by means of isotope exchange reactions occurring on catalyst surface. The use of permselective Pd-based membrane allows withdrawal of reactions products all along the reactor, and thus limits reverse reaction rate to the benefit of the direct one (shift effect). The reactions kinetics, which are still little known or unknown, are generally assumed to be largely greater than the permeation ones so that thermodynamic equilibriums of isotope exchange reactions are generally assumed. This paper proposes a new phenomenological 2D model to represent catalytic membrane reactor behavior with the determination of gas effluents compositions. A good agreement was obtained between the simulation results and experimental measurements performed on a dedicated facility. Furthermore, the gas composition estimation permits to interpret unexpected behavior of the catalytic membrane reactor. In the next future, further sensitivity analysis will be performed to determine the limits of the model and a kinetics study will be conducted to assess the thermodynamic equilibrium of reactions.

1. Introduction

During its lifecycle, a D–T fusion machine will produce amounts of tritiated waste of various activities and natures[1]. Several issues associated to tritiated waste management have been pointed out since 1997 as a result of the DTE1 experiments done in the JET machine[2]. Thus, for economic and environmental reasons, sev-eral processes have been developed since decades either to recover volatile tritiated species (Q2 and/or Q2O where Q = H, D or T) as

fusion fuel or to trap them by for instance oxidation/adsorption processes[3].

A promising intensified process considered for the recovery of tritium uses combined effects of catalytic conversion and selective membrane purification properties. Even though efficiency of such a process has already been demonstrated either on soft housekeeping waste[4]or highly tritiated water effluents[5], some mechanisms, particularly in terms of reaction conversions are not really well known yet. Considering deuterium as tritium tracer, the overall set of reactions occurring with a Q2/Q2O mixture is given below:

D2O + H2⇋HDO + HD (R1) HDO + H2⇋H₂O + HD (R2)

H2+D2⇋2 × HD (R3) D2O + H2⇋H₂O + D₂ (R4) HDO + D2⇋D₂O + HD (R5) H2O + D2⇋HDO + HD (R6) 2HDO ⇋ H2O + D2O (R7)

From the above reversible reaction set, two possible chemical pathways appear: if reactions’ thermodynamic equilibriums are reached,(R1)–(R3)reactions are sufficient to describe the whole system. Indeed,(R4)–(R7)equilibrium constants are linear com-binations of the three others. Nevertheless, if chemical reacting system is rate limited, kinetics of each of the 7 reactions must be considered. Considering the fact that above a temperature of nearly 100◦_{C reactions(R1)–(R3)have reached their}

thermody-namic equilibriums, most of catalytic membrane reactor models have neglected the reactions kinetics[6–8]. Based on this assump-tion, a new phenomenological model is proposed including gaseous effluents speciation. Results of this model are compared to experi-mental results obtained on a dedicated facility.

2. Experimental facility

An experimental test bench has been built at CEA Cadarache to perform parametric study on catalytic membrane reactors.Fig. 1

gives a schematic view of the instrumented experimental device; a detailed description of the process has already been reported

[9]. Diluted deuterated feed stream, composed of binary mix-tures of N2 and D2O, is fed to the lumen side of a finger-type

catalytic membrane reactor containing about 20 g of commercial Ni-Based catalyst pellets (NiSAT®_{310RSCDS). The membrane tube}

(length = 48.5 cm, outer diameter = 1 cm, wall thickness = 150 mm) is made of a defect free Pd77Ag23 alloy allowing only hydrogen

isotopes permeation. The feed stream reacts with permeated pro-tium coming from the counter-current sweep stream. Deuterium hydride and dideuterium produced are partially removed from the lumen side by counterdiffusion through the membrane and with-drawn by the permeate stream. Remaining reaction products are removed by the retentate stream.

Fig. 1. Detailed instrumentation plan of the facility.

Calibration of the analysis chain is described in[9]. Combin-ing the composition measurements with the streams total flow rates allowed to track molecular and atomic species from any inlet to any outlet of the catalytic membrane reactor. Because of mea-surement errors and to compare measured and calculated values,

data reconciliation on raw measurements results was done. A max-imal deviation of 7% was encountered between raw and reconciled measurements.

3. Modeling approach

The design of the catalytic membrane reactor permits to define 2 zones (the lumen and the shell) to be considered for the mass balance, both zones being separated by the membrane in through which permeation occurs. Considering that:

•_{the profiles along the reactor’s centerline are axis-symmetric} (

∂

/

∂

 = 0);

•_{the entire module is isothermal (}

_∂

_/

_∂

_{T = 0);} •_{the lumen’s pressure-drop can be neglected;}

•_{the thermodynamic behavior is described by ideal gas equation} of state and the gas is assumed to be incompressible;

•the membrane is defect free (infinite selectivity toward protium and deuterium);

•_{the chemical reactions occur at the catalyst surface and} thermo-dynamic equilibrium is assumed at any point of the lumen; •_{the catalyst is assumed to be composed of monodisperse}

cylin-drical particles.

Then, for each species i, the mass balance can be written for the lumen and the shell sides.

3.1. Mass balance in the lumen

For each species i, the mass balance is represented in the gas phase by: ε∂C lumen i ∂t −ur ∂Clumen i ∂r +uz ∂Clumen i ∂z =ε∂ ∂z



Dax,i ∂Clumen i ∂z



+1 r ∂ ∂r



εDrad,i ∂Clumen i ∂r



−_kg,iav C_ilumen−C ∗ i

(1) where Cilumen is the concentration of species i in the lumen

(mol/m3_{), « is the fixed bed porosity (−), u}

rand uzare, respectively,

the radial and axial velocity (m/s), Dax,iand Drad,iare, respectively,

the axial and radial dispersion coefficient (m2_{/s), k}

g,iis the external

mass transfer coefficient (m/s), avis the specific area of the catalyst

(m2_/m3_).

On the left hand side of Eq.(1)are represented the terms cor-responding to the evolution of the concentration of the species i towards time and the mass transfer of species i in the volume. Due to the permeation phenomena, the radial mass transfer cannot be neglected. On the right hand side are represented the mass trans-fer of species i in the volume due to axial/radial dispersion and the mass transfer of species i from the gas phase to the catalyst surface. The velocity field is obtained by means of Navier Stokes equations, considering that porous media has average values of porosity ε and permeability  on the cell. Radial voidage profile is estimated by the empirical correlation of Hunt and Tien[10].

The mass balance on the surface of the catalyst considers that the evolution of the concentration of species i at the surface of the catalyst is a balance between the flux of species coming from the gas phase and the flux of species i consumed by the reactions (Eq.

(2)). ∂C∗ i ∂t −kg,iav C lumen i −C ∗ i

=(1 − ε) pRi (2)

where Ci*is the concentration of species i at the surface of the

cata-lyst (mol/m3_{), }

pis the density of the catalyst (kg/m3), Riis the total

flux of species i consumed by the reactions (mol/kg catalyst/s). Rican be linked to the fluxes of species i consumed by each

specific reaction j (rs,j) by means of:

Ri=

nb reactions

X

j=1

i,jrs,j (3)

where i,jis the stoichiometric coefficient of species i in the reaction

j and rs,jis the flux of species i consumed by reaction j (mol/kg

cata-lyst/s). Considering that the thermodynamic equilibrium has been reached for each reaction, rs,jcan be written under the form below

where Kjis the equilibrium constant and kjthe kinetics constant (kj

is assumed to be high enough so that thermodynamic equilibrium is reached). rs,j=kj

!

_nbreagents

Y

i=1 Clumen





i,j





i − 1 Kj nbproducts

Y

k=1 Clumen





k,j





k

#

3.2. Mass balance in the shell

For each species i, the mass balance is represented in the gas phase by: ∂Cshell i ∂t +



v

_r ∂Cshell i ∂r +

v

z ∂Cshell i ∂z



= ∂ ∂z



Dm_i ∂C shell i ∂z



+1 r ∂ ∂r



Dm_i ∂C shell i ∂r



(4) where Cishellis the concentration of species i in the shell (mol/m3),

v

_rand

v

_zare, respectively, the radial and axial velocity (m/s), D_imis the diffusion coefficient of species i in the mixture (m2_/s).

On the left hand side of Eq.(4)are represented the terms cor-responding to the evolution of the concentration of the species i towards time and the mass transfer of species i in the volume. On the right hand side are represented the mass transfer by diffusion of species i in the volume.

The velocity field is obtained by means of Navier Stokes equa-tions.

3.3. Boundary conditions and initialization

Initial conditions for the systems consider that at t = 0, the con-centrations are null in the whole volume except at the lumen and shell inlets where the concentrations are, respectively, equal to the composition of the deuterated fluid and the composition of the swamping gas.

The classical Danckwerts boundary conditions are used for the inlet and outlet of the catalytic membrane reactor[11]. Consid-ering that the concentration profile is established at the inlet of the bleedoff tube, that species cannot permeate through the bleed-off tube and through the tap on which the spring is fixed, that the concentration profile in the lumen is axisymmetric and that only hydrogen isotopes can permeate through the membrane, one can established the boundary conditions for the lumen side (see

Table 1). The isotope permeation flux density (Jimembmol/m2/s)

through the membrane is equal to zero for all species except for the hydrogen isotopes for which the following equation is used (Richardson law[12]): Jmemb_i = i 2ı

q

Plumen i −

q

Pshell i



(5)

where ı is the membrane thickness (m), Pilumen and Pishell are,

respectively, the partial pressure of species i in the lumen and in the shell (Pa) and iis the permeability of species i in the

mem-brane (mol/m/s/Pa0.5_{). Note that for HD, the previous equation}

cannot be used as permeation is a phenomenon which involves atomic species. In the case of HD, H and D have different diffusion coefficients which have an effect on the composition of adsorbed species at the membrane surface before recombination. Hence, for the HD permeation flux density, it is proposed to use the following equation[13,14]: Jperm_HD =

q

4 Jmemb H₂ JDmemb₂ (6) Table 1

Boundary conditions for the lumen side.

Domain Boundary condition z = 0 ∀r ∈ [rbleedoff; rmemb] C_ilumen=Cinlet

i z = Lbleedoff ∀r ∈ [0; rbleedoff] ∂Cilumen/∂z

=0 r = rbleedoff ∀z ∈ [0; Lbleedoff] urClumen_i −_εDrad,i ∂Clumen

i /∂r

=0 z = Lmemb ∀r ∈ [0; rmemb] uzC_ilumen−εDax,i ∂Cilumen/∂z

=0 r = 0 ∀z ∈ [Lbleedoff; Lmemb] ∂C_ilumen/∂r

=0

r = rmemb ∀z ∈ [0; Lmemb] urClumen_i −εDrad,i ∂C_ilumen/∂r

=Jmemb i

Considering that the concentration profile is established at the outlet of the shell, that species cannot permeate through the wall of the shell and through the tap on which the spring is fixed and that only hydrogen isotopes can permeate through the membrane, one can establish the boundary conditions for the shell side (see

Table 2below):

Table 2

Boundary conditions for the shell side.

Domain Boundary condition

z = Lmemb ∀r ∈ [rmemb; rshell] Cishell=C shell i z = 0 ∀r ∈ [rmemb; rshell] ∂Cishell/∂z

=0 r = rshell ∀z ∈ [0; Lshell] v_rCshell

i −D m i ∂C shell i /∂r

=0 r = rmemb ∀z ∈ [0; Lmemb] v_rCshell

i −D m i ∂C shell i /∂r

= −Jmemb i 3.4. Parameters

Considering that the thermodynamic equilibrium is reached for all chemical reactions, equilibrium constants for reaction(R1)–(R3)

were estimated using a thermodynamic approach.

Assuming ideal gas equation of state and a generic reaction aA + bB ⇋ cC + dD, the equilibrium constant can be estimated

by: K = d

Y

i=a Pii=exp



−1rg 0_{(T )} RT



(7)

The reaction free enthalpy 1rg0(T ) J/mol

is defined as[15]:

1rg0(T ) = 1rh0(T ) − T1rs0(T ) With: •_1rh0_{(T ) =}
rh0(Tref) + T

Z

T_ref

X

i iCpi(T ) dT

•_1rh0_(T ref) =

X

i ni 1rh0_f,i(Tref) And: •_1rs0_{(T ) = 1} rs0(Tref) + T

Z

T_ref

X

i iCpi T dT •_1rs0_(T ref) =

X

i i s0i(Tref)

In the previous equations, 1rh0(T ) is the standard enthalpy

of reaction (J/mol) at temperature T, 1rh0_f,i(Tref) is the standard

enthalpy of formation of species i at Tref(J/mol), Cpiis the specific

heat capacity of species i (J/mol/K), 1rs0(T ) is the standard entropy

of reaction (J/mol/K) at temperature T and s0

i(Tref) is the entropy

of species i at temperature Tref(J/mol/K).

Thermophysical properties required for the estimation of the equilibrium constants can be found in the DIPPR801 Database from AIChE and NIST database. This leads to the following evolution of the equilibrium constants with temperature (Fig. 2).

Fig. 2. Equilibrium constants evolution with T.

The permeabilities of protium and deuterium in the membrane were determined in a previous study [9] and are given in the

Table 3below.

Table 3

Permeabilities of H and D in Pd77Ag23membrane.

Species i Permeability i(mol/m/s/Pa0.5) H 6.1210−8exp − 6876/RT

D 4.9310−8_{exp − 7965/RT}

The other parameters were estimated using correlations established in former studies (seeTable 4).

Table 4

Mass transfer parameters.

Parameter Reference

Dm

i (non polar mixture) Chapman-Enskog[16] Dmi (polar mixture) Brokaw[17] Dax,i and Drad,i Gunn[18]

kg,i Yoshida et al.[19]

4. Modeling assessment

The partial differential equations system defined in Section3

was implemented in COMSOL Multiphysics®_{4.3a commercial code}

and resolved by PARDISO solver. Results of the simulation were compared to experimental results obtained on the facility described in Section 2. Experiments were performed at 320◦_{C for several}

compositions of the feed stream composed of nitrogen and D2O

in the range of 0.1 to 4 molar%. The feed stream and swamping gas flowrates were 100 N ml/min. The lumen and shell pressures were, respectively 2.5 bar and 0.5 bar. For each experiment, the dedeuter-ation factor (DF) was determined as the ratio of the amount of deuterium in the feed stream to the amount of remaining deu-terium leaving the lumen[20].Fig. 3presents the modeling results in red and the experimental ones in blue bullets.

Fig. 3. Evolution of the dedeuteration faction.

The evolution of the DF with the D2O amount in the feed steam

shows a maximum at nearly 1.5 molar% of D2O. The increase of DF

when D2O amount increases could not be easily foreseen without

detailed knowledge of the phenomena occurring in the catalytic membrane reactor. But it can be noted that the model results present a good agreement with experimental measurements.

The evolution of DF could not be interpreted without the gaseous streams compositions measurements or estimations.Fig. 4shows the evolution of the relative amounts of deuterated species in the lumen output (compared to deuterated species amount in the lumen input) versus the amount of D2O in the feed stream.

Fig. 4. Evolution of lumen output composition (bar graphs are experimental values; areas are model results).

Below 1.5 molar% D2O in the feed stream, only few amounts

of HDO or D2O remain in the lumen at the output of the

reac-tor indicating an efficient conversion of D2O. In the meantime,

the relative amount of HD at the output of the lumen decreases with an increase of the D2O input. This can be explained by an

increase of the HD permeation flux as the partial pressure of HD coming from D2O conversion increases in the lumen. The

combi-nation of the improvement of the HD permeation and the efficient conversion of D2O leads to an improvement of DF as shown on

Fig. 3.

Above 1.5 molar% D2O in the feed stream, the presence of

HDO at the output of the lumen increases significantly indicat-ing a depletion of D2O conversion leading to a decrease of DF

(seeFig. 3). It is then clearly demonstrated that above 1.5 molar% D2O in the feed stream, the permeation flux of hydrogen is not

sufficient enough to allow a full conversion of D2O and that an

increase of the partial pressure of hydrogen in the shell side will be necessary to improve the catalytic membrane reactor efficiency.

Finally, the comparison between experimental results and model ones onFigs. 3 and 4shows the good predictive ability of the model.

5. Conclusion

In this paper, a new 2D modeling approach is proposed to rep-resent the behavior of a catalytic membrane reactor including the estimation of the lumen and shell outputs composition.

The comparison of the model prediction with experimental data have shown a good agreement and the gas phases speciation estimation permits to interpret non trivial behavior of the catalytic membrane reactor. In the next future, further sensitivity analysis will be performed to determine the limits of the model and a kinetics study will be conducted to assess the thermodynamic equilibrium of reactions. However, the model proposed seems already very promising.

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